Yes, it can be intermittently broken. Testing is the surest way. Anyways, your videos showed cranking taking 3.5-4 seconds, not 7-10 as you say. It's not that I don't believe you, but I counted the time on the video.

Fuel problems - ok, fuel problems are something else. When you start the car and put the key in the ignition, the fuel pump starts up. You should immediately have fuel for the engine when you crank. Fuel pumps rarely break intermitterntly. Same with Fuel Filters. With an SRT6, with its high gasoline needs, your car would be dying all the time if either of those units were at fault. When you turn the key to position 1, you should hear a "whirring" noise. That is a combination of a few things making noise but one is your fuel pump. It is shooting fuel through your fuel system and that is on an open loop through the injector fuel rails back to the fuel tank. You should be getting fuel.

OK, assuming that your ECU isn't broken then either your car isn't getting spark or it's not getting air. You don't have VALVETRONIC or anything on this car it is a good old fashioned throttle body, so you're getting air. Which means that your engine isn't sparking. If your engine isn't sparking, then we have to think about your coil packs, wires or plugs. Since this car is coil on plug, probably not wires and probably not coils. So the other thing that the engine uses to start spark is to read the timing on the car by use of the Crankshaft Position Sensor.

CEL - OK, you didn't mention this before and this is good. This means that your engine threw a code and now you must get the code read. Go to autozone, pep boys or checkers and ask for a code-reading tool. They will give you one for free to use. BTW, a good OBD2 scanner should be able to show you fuel rail pressure so take note if you can!!! My bet is on ECU Code "O2 Sensor reading low/high" something to that effect.